Once you have your device highlighted, click "Podcasts" in the top navigation bar and sync the podcasts you want on your device. Click "apply" and the episodes you have downloaded on your iTunes software will sync with your device.

that's it!

The beauty of this process is that now, every new episode of your subscribed podcasts will automatically sync to your device every time you plug it in and open iTunes. You can now take your favorite shows with you everywhere you go.